**Practical Methods of Financial Engineering and Risk Management Tools for Modern Financial Professionals by Rupak Chatterjee**

## Contents of Financial Engineering and Risk Management

- Chapter 1. Financial Instruments
- Chapter 2. Building a Yield Curve
- Chapter 3. Statistical Analysis of Financial Data
- Chapter 4. Stochastic Processes
- Chapter 5. Optimal Hedging Monte Carlo Methods
- Chapter 6. Introduction to Credit Derivatives
- Chapter 7. Risk Types CVA Basel III and OIS Discounting
- Chapter 8. Power Laws and Extreme Value Theory
- Chapter 9. Hedge Fund Replication

## Chapter Descriptions

**Chapter 1 **(“Financial Instruments”) describes several basic U.S. financial instruments that drive all asset classes in one way or another.

I present these instruments in the universal form in which Wall Street traders interact with them: Bloomberg Terminal screens.

The ability to read quotes from these screens is a matter of basic literacy on any Wall Street trading floor.

**Chapter 2 **(“Building a Yield Curve”) describes the generic algorithm for building LIBOR-based yield curves from cash instruments, futures, and swaps.

Yield curve construction is often described as simply “getting zero coupon rates.” In reality, this is far from true. On Wall Street, a yield curve is a set of discount factors, not rates.

All firms need the ability to calculate the present value (PV) of future cash flows using discount factors in various currencies.

The techniques described in this chapter are widely used in the industry for all major currencies. The increasingly important OIS discounting curve is described in Chapter 7

**Chapter 3** (“Statistical Analysis of Financial Data”) introduces various fundamental tools in probability theory that are used to analyze financial data.

The chapter deals with calibrating distributions to real financial data. A thorough understanding of this material is needed to fully appreciate the remaining chapters.

I have trained many new analysts at various Wall Street firms. All these fresh analysts knew probability theory very well, but almost none of them knew how to use it.

Chapter 3 introduces key risk concepts such as fattailed distributions, the term structure of statistics, and volatility clustering. A discussion of dynamic portfolio theory is used to demonstrate many of the key concepts developed in the chapter.

This chapter is of great importance to implementing risk management in terms of the probabilities that are typically used in real-world risk valuation systems—value at risk (VaR), conditional value at risk (CVaR), and Basel II/III—as opposed to the risk-neutral probabilities used in traditional front-office systems.

**Chapter 4 **(“Stochastic Processes”) discusses stochastic processes, paying close attention to the GARCH(1,1) fat-tailed processes that are often used for VaR and CVaR calculations.

Further examples are discussed in the realm of systematic trading strategies. Here a simple statistical arbitrage strategy is explained to demonstrate the power of modeling pairs trading via a mean-reverting stochastic process.

The Monte Carlo techniques explained in this chapter are used throughout Wall Street for risk management purposes and for regulatory use such as in Basel II and III.

**Chapter 5 **(“Optimal Hedging Monte Carlo Methods”) introduces a very modern research area in derivatives pricing: the optimal hedging Monte Carlo (OHMC) method.

This is an advanced derivative pricing methodology that deals with all the real-life trading problems often ignored by both Wall Street and academic researchers: discrete time hedging, quantification of hedging errors, hedge slippage, rare events, gap risk, transaction costs, liquidity costs, risk capital, and so on.

It is a realistic framework that takes into account real-world financial conditions, as opposed to hiding behind the fictitious assumptions of the risk-neutral Black-Scholes world.

**Chapter 6 **(“Introduction to Credit Derivatives”) introduces credit derivatives, paying special attention to the models needed for the Basel II and III calculations presented in Chapter 7.

All the standard contract methodologies for credit default swaps (CDS) are described with a view to elucidating their market quotes for pricing and hedging.

Asset swaps, collateralization, and the OHMC method applied to CDS contracts are also discussed

**Chapter 7 **(“Risk Types, CVA, Basel III, and OIS Discounting”) is a very timely and pertinent chapter on the various new financial regulations that have affected and will continue to affect Wall Street for the foreseeable future.

Every Wall Street firm is scrambling to understand and implement the requirements of Basel II and III and CVA.

Knowledge of these topics is essential for working within the risk management division of a bank. The effect of counterparty credit risk on discounting and the increasingly important use of OIS discounting to address these issues is also presented.

**Chapter 8** (“Power Laws and Extreme Value Theory”) describes power-law techniques for pinpointing rare and extreme moves.

Power-law distributions are often used to better represent the statistical tail properties of financial data that are not described by standard distributions.

This chapter describes how power laws can be used to capture rare events and incorporate them into VaR and CVaR calculations.

**Chapter 9 **(“Hedge Fund Replication”) deals with the concept of asset replication through Kalman filtering. The Kalman filter is a mathematical method used to estimate the true value of a hidden state given only a sequence of noisy observations.

Many prestigious financial indices and hedge funds erect high barriers to market participants or charge exorbitant fees.

The idea here is to replicate the returns of these assets with a portfolio that provides a lower fee structure, easier access, and better liquidity.